On February 1,
1997 the Station Casino St. Charles which is located on the
banks of the Missouri River in a western suburb of St. Louis
began offering a handful of tables of double deck Blackjack.
The rules are the same as their six-deck game: dealer hits A-6,
double on any first two cards, resplit pairs up to 4 times (and,
effective March 3, resplit Aces as well) and double after split.
Most of the tables are $25-$500, but there are usually one or
two with a $10 minimum. The casino has an edge of .35% over
the basic strategy player and the game is cut at the 75% penetration
point and it's dealt from a shoe (a Missouri Gaming Commission
rule) with all cards face up.
Basic Strategy
Variations
I have never played
double deck before for any length of time, so I knew I'd have
to do some homework to get ready. The basic strategy for double
deck is the same for 4 or 6 decks, so there was not a lot there
which I needed to work on. However, unlike the 6-deck games
where I get up when the true count is -1 or lower, I knew I'd
have to play through all the double deck shoes, so I'd need
to learn more of the 'minus' indexes in the basic strategy variations.
For example, in a six-deck game, I'd be long gone before I'd
have to play a 13 against a dealer's 5 in a highly negative
count. But, one should hit a 13 vs. 5 at -4 and I needed to
learn that. I added all the plays from -3 to -6 to my pack of
flashcards which covers -2 to +10 and began to learn all the
basic strategy variations from -6 to +10.
Money Management
Next I had to
work out a betting schedule. I always like to use an example
of a betting schedule based on a $3000 bankroll so, even though
I actually use a multiple of that, I'll break everything down
to that size so you can see how it will work with a minimum
bankroll. The casino has a starting edge of .35% now that resplit
of Aces is allowed; it was .40% and since each increase of 1
in the true count is worth .5%, at a true count of 1 I'd have
a small edge over the casino. Since I'd be playing at a $10
table, I'd be over betting somewhat until the true hit 2, but
there was no choice in the matter. Because double after split
is allowed, my optimum bet would be 76% of my advantage. If
this is confusing to you, reread the section on money management
which begins at Lesson 7. Here's a table I use to calculate
the optimum bet:
| True Count
|
Advantage
|
Optimum
Bet |
| 0 or lower
|
(.35+) |
0 |
| 1 |
.15% X .76
|
.00114 |
| 2 |
.65% X .76
|
.00494 |
| 3 |
1.15% X .76 |
.00874 |
| 4 |
1.65% X .76 |
.01254 |
| 5 |
2.15% X .76 |
.01634 |
| 6 |
2.65% X .76 |
.02014 |
| 7 |
3.15% X .76 |
.02394 |
| 8 |
3.65% X .76 |
.02774< |
Following me on
this? At the beginning of a shoe, the casino has an advantage
of .35% because of the rules of their game and the fact that
they're dealing from 2 decks. If the count goes minus, their
edge will increase and the OPTIMUM bet in that situation is
$0. That's not the PRACTICAL bet, however, since it's a $10
minimum table, so I have to bet that amount. As the count goes
up, I can bet the prescribed percentage of my bankroll as indicated.
For example, with a $3000 bankroll, my optimum bet at a true
count of 3 is .00874 X $3000 = $26.22. Here's how the chart
looks for a $3000 bankroll:
| True Count |
% Optimum
Bet |
Optimum
Bet |
| 0 or lower
|
0 |
$ 0 |
| 1 |
.00114 X $3000
|
$ 3.42 |
| 2 |
.00494 X $3000 |
$ 14.82 |
| 3 |
.00874 X $3000
|
$ 26.22 |
| 4 |
.01254 X $3000 |
$ 37.62 |
| 5 |
.01634 X $3000
|
$ 49.02 |
| 6 |
.02014 X $3000
|
$ 60.42 |
| 7 |
.02394 X $3000 |
$ 71.82 |
| 8 |
.02774 X $3000
|
$ 83.22 |
That's the theoretical,
not the practical. As I stated before, I must bet at least $10
and I really feel strongly about the fact that the top bet should
not exceed 2% of the total bankroll, so I end up with a $10-60
spread until the bankroll gets bigger. A 1 to 6 spread can beat
this game, but there's a nice little trick I can use to get
more money on the table without increasing my risk too much:
play 2 hands in positive situations. Here we go with more math,
but stick with me; it's important.
Since I would,
whenever appropriate, play 2 hands, I'd need a table for the
optimum bets for those situations. The rule here is that 56%
of the advantage times the bankroll is the optimum bet for each
of two hands. In other words, if it's correct for me to bet
$25 on one hand, I would be over betting if I bet $25 on each
of two hands at the same true count. Because of covariance (the
relationship of two hands to one another), the optimum bet must
be reduced. Since I must bet at least $10 on each hand (Casino
Station St. Charles doesn't have that silly rule that a player
must bet twice the minimum on each hand when playing more than
one; many do, so check), it's practical for me to spread to
two hands of play only when the true count is at 2 or more.
Here's how that chart looks:
| True Count |
% Advantage
|
Optimum
Bet for Two Hands |
| 2 |
0.65% X .56
|
.00364 |
| 3 |
1.15% X .56
|
.00644 |
| 4 |
1.65% X .56
|
.00924 |
| 5 |
2.65% X .56
|
.01484 |
| 6 |
3.15% X .56 |
.01764 |
| 7 |
3.65% X .56
|
.02044 |
| 8 |
4.15% X .56 |
.02324 |
Factoring this
with a $3000 bankroll gives us the optimum bet for each of two
simultaneous hands at different positive counts:
| True
Count |
%
Optimum Bet |
Optimum
Bet for Two Hands |
|
2 |
.00364
X $3000 |
$
10.92 |
| 3 |
.00644
X $3000 |
$
19.32 |
| 4
|
.00924
X $3000 |
$
27.72 |
| 5 |
.01484 X $3000 |
$ 44.52 |
| 6 |
.01764 X $3000 |
$ 52.92 |
| 7 |
.02044 X $3000 |
$ 61.32 |
| 8
|
.02324 X $3000 |
$ 69.72
|
At Last! The Betting Schedule
Obviously I cannot place a bet
of $10.92 so I'll have to round things off in order to arrive
at a practical betting schedule. In doing that, I keep several
things in mind. First, I want a schedule which will allow me
to 'parlay' winning bets as the count goes up. For example,
if the bet for a true count of 2 is $20, it would be great if
the bet for a true count of 3 was twice that; it makes me look
like a 'gambler' to just add my winnings to the original bet.
Of course I'd only be doing it because the count has gone up,
but it's something to keep in mind as I design the schedule.
Another 'nice-to-have' thing is a schedule which allows me to
bet some multiple of the true count. For example, "$10 times
the true" would mean that at a true of 2 my bet would be $20,
at a true of 4 it'd be $40, etc. Another point to keep in mind
is that we have a bit of a 'fudge' factor built into counts
above 2.4 in a double deck game. Why 2.4? Well, that's the true
count at which one should take insurance in a double deck game
and that option is so valuable that it adds to our advantage.
While the advantage goes up about .5% with each increase of
1 in the true count, above 2.4 the advantage increase is more
like .58%. So our 'real' advantage at a true of 7 is more like
4% than the 3.65% which I show on the charts above. This gives
us a cushion for rounding up a bit.
So, here's the betting schedule
I worked out for a $3000 bankroll. Bear in mind that as the
bankroll increases (or decreases), the schedule must be changed
in order to keep the risk of 'gambler's ruin' about the same.
I will modify the schedule at $1000 increments; that is, if
I win $1000, I'll refigure the betting schedule by remultiplying
all the percentages by $4000. On the other hand, if I choose
to spend my profits, I'll just continue to operate with the
original schedule. In the unlikely event that I hit a big losing
streak (how's that for positive thinking?) I really couldn't
downsize the bets very much. As long as the bank remains above
$2000, I'll stick with this schedule. If it should go below
$2000, I'd quit until I could build the bank up again.
Betting Schedule $3000 Bank
- Double Deck
(DOA; DAS; RSA; Dlr hits A-6) |
| True Count |
Bet: One hand |
Two Hands |
| 0 or lower |
$10 |
N.A. |
| 1 |
$10 |
N.A. |
| 2 |
$15 |
$10 |
| 3 |
$25 |
$20 |
| 4 |
$40 |
$30 |
| 5 |
$50 |
$40 |
| 6 or higher |
$60 |
$50 |
Notice that I top out at one hand
of $60 or 2 hands of $50, regardless of how high the count gets.
I'll stick with that until the bankroll increases and I get
a 'feel' for just how the floor supervisors at the casino react
to such a spread. The 'pit critters' know that counters vary
their bets widely, so I'm going to be conservative for a while
since this is my 'home'. If I was playing this game somewhere
else -- where they wouldn't see me for months at a time -- I'd
be more aggressive. The single-hand schedule is not an easy
to memorize; it's not a straight parlay and it's not a simple
multiple of the true count. I'm going to be screwing around
a lot with $5 and $25 chips and precise betting is another indicator
of a card counter, so I may find myself 'pushing' the count;
that is, over betting a bit on a true of 2 or 3. I'll have to
watch that, since my reaction will be to bet $20 on a true of
2 and $30 on a true of 3. With that, the schedule is $10 times
the true, but a bank of $4000 is required to justify those bets.
I'll just have to see how it goes.
Playing Two Hands
Whether or not one should play
one or two hands is more a factor of opportunity than strategy.
If there is no space available at the table for a second hand,
I obviously must play only one. Neither am I going to play two
hands when the true count is below 2, nor am I going to play
two hands if I'm alone with the dealer. The reason for that
last rule is twofold: First, by playing a second hand, more
cards are used and -- since I only go to two hands on positive
counts -- I'll be 'eating' good cards. That's okay, but when
head-to-head with the dealer, my two hands represent an increase
in the total bet of about 150% but I'm also using up 150% more
of the cards. Second, the game has a high maximum bet, well
above my maximum so I don't need to spread to two hands in order
to get more money on the table. So, whenever I'm alone and the
table limit is above my top bet, I'll always play one hand.
If there is at least one other
player besides me at the table, I'll then spread to two hands
whenever possible. In that case I do want to 'eat' the good
cards; why give the opportunities to others when I can get them
for myself? Mercenary, perhaps but this IS about money, you
know.
Lots of gamblers play two hands,
so the maneuver won't draw a lot of attention to you unless
you make a big deal about it. First, most casinos allow two
hands only if they are located in two adjacent betting circles.
If you're sitting at 'first base', don't try to place a second
bet at the empty spot on third base. Also, I don't ask people
to move to the next spot over in order to accommodate my second
hand and I never refuse to allow someone else to sit down and
play in the spot I was using for my second hand. You have to
look indifferent about the idea of a second hand -- just like
a gambler would. One neat trick is to spread to two hands when
a new player joins the table (assuming of course that the count
justifies it); gamblers seem to think that doing so 'keeps the
cards in proper order' when someone is jumping in and out. Naturally
it's BS, but anything that makes me look more like a gambler
is welcomed.
Practice Makes Perfect
Next I had to set up a regimen
of practice to get used to playing a double-deck game. I already
own several decks of cards from the casino, so I can use them
to 'calibrate' my eyes for estimating the number of decks left
to be played. I did this to a half-deck accuracy and can consistently
cut 26 cards from two decks shuffled together. I accomplished
this simply by breaking the pack into four parts over and over
again and counting the segments when I was done. Just looking
at a half-deck, a full deck and a deck and a half gets you used
to estimating the number of cards remaining to be played. It's
hard to describe until you try it for yourself, but I think
you know what I mean. I also did some mental calculations of
dividing various running counts by 1.5 and .5, etc. to get used
to figuring the true count.
I further practiced by counting
down two decks to check my accuracy; I can do it in 22 seconds
which is more than ample for casino conditions.
But the practice I did most was
with a program called "Blackjack Professor" which I set up to
reproduce the conditions and rules for the game at Station Casino
St. Charles. Whenever I had a spare hour or so I played the
game, which is dealt on a head-to-head basis with no other players,
utilizing my betting schedule and the other techniques which
I use in the casino. For example, if I had $10 bet and the count
jumped up considerably, as it will near the end of a shoe, I
would not come out with a $40 bet on the next hand, since I
wouldn't likely do that at the casino. I'd bet $20 instead and
then go to $40 on the next hand, if there was a next hand. Conversely,
if I 'pushed' a hand and the count had dropped dramatically,
I'd leave the bet out there, just as I would do in the casino.
By doing all that, I felt my results from practice would be
similar to what I could expect in the casino. Here are the results
of 6 different sessions on the computer. Remember, I played
each hand according to the basic strategy variations and I bet
according to the schedule above, though I never spread to 2
hands because I was always alone at the table. The earnings
per hour are based on a rate of 60 hands an hour, a much more
realistic figure than the 300 hands an hour I was able to play
on my computer.
| Session |
# of hands |
% won |
$ won |
$/hour |
% advantage |
| 1 |
276 |
48.03% |
65.00 |
$14.13 |
1.60% |
| 2 |
596 |
47.42% |
135.00 |
$13.59 |
1.39% |
| 3 |
566 |
45.05% |
272.50 |
$28.89 |
2.99% |
| 4 |
472 |
43.54% |
(345.00) |
($43.86) |
(4.43%) |
| 5 |
1773 |
46.36% |
(940.00) |
($31.81) |
(3.03%) |
| 6 |
920 |
51.14% |
1302.50 |
$84.95 |
8.35% |
This totals to 4603 hands which
represents about 76 hours of casino time and a profit of $490
or $6.44 an hour. From the program, I was able to extrapolate
that my average bet size is about $14, so my overall advantage
for these 6 sessions works out to be about .76% which is about
half of what I would expect in a bigger sample size. My big
losing session saw me reach a low of about $1050 which is not
surprising. The lesson to learn from these simulations is that
"the money in Blackjack comes in chunks." To anticipate a steady
income from this game is a big mistake; you can easily see how
wild the swings are.
Actual Play
All the above is theoretical;
what matters are real results from actual casino play. To date
I've played 7 sessions and here are the results, based on a
$10 to $60 spread:
| Session 1 |
2.5 hours |
($110) |
| Session 2 |
1.5 hours |
($410) |
| Session 3 |
2.0 hours |
$240 |
| Session 4 |
2.0 hours |
$250 |
| Session 5 |
3.0 hours |
$355 |
| Session 6 |
3.0 hours |
$205 |
| Session 7 |
2.5 hours |
($260) |
These actual playing sessions total
16.5 hours of play and a profit of $270 for an hourly income
of $16.36. I must add that the first two sessions were played
before I had fully developed my betting schedule and before
I had put in a lot of practice time. I will freely admit that
those two loses were a 'wake-up' call that I needed to spend
some time practicing the double-deck game, even though double
deck is MUCH more closely related to 6 decks than it is to single
deck. Once I got 'in the groove', my results are about as I
expected. If we ignore those first two sessions, I've won $790
in 12.5 hours for an hourly rate of $63.20. That number cannot
be sustained, but it's very typical of how this whole thing
works. Over the coming months, I'll probably win about 65% of
my sessions and lose or break even in the rest. The hourly income
will drop to a more realistic $20 or so, assuming I don't increase
the bank size. That's not enough to retire on, but it is a nice
part time job.
I hope the thought processes which
I've tried to show in this lesson give you an insight into how
to structure a plan for your own play. I guess the only 'sage'
advice I have at this point is that you must practice a lot
more than you play to be successful at this game.
This concludes my series, but
I hope you'll stay in touch.
